Total Lift Coefficient Research Articles

Numerical investigation of fluid flow and heat transfer of a nanofluid around two circular cylinders arranged in tandem in horizontal duct

In this study, two-dimensional unsteady laminar convective heat transfer from two isothermal cylinders arranged in tandem in horizontal duct has been numerically investigated. The numerical study is performed by solving the governing equations (continuity and momentum) and energy equations using a finite volume-based code ANSYS Fluent. The present study was conducted using nano sized copper particles suspended in water. The Prandtl number Pr of the resulting suspension being equal to 7. The range of solid volume fractions studied is and the flow Reynolds number is equal to 100.The spacing ratio of the two cylinders was varied from 2 to 5 while the blockage ratio was kept constant β=0.25. A detailed discussion has been provided regarding the variation of flow structure and the characteristics of flow, including total drag and lift coefficients, as a function of the dimensionless parametersIn order to visualize the flow and heat transport, streamlines, vorticity contours and isotherms were generated. In addition, the local and average Nusselt numbers for the upstream and downstream cylinders are calculated. The results demonstrate that the force coefficients, the wake structure behind the cylinders, and the Nusselt number are significantly influenced by the value of the spacing ratio and the volume fractions of nanoparticles. The results demonstrate a significant enhancement in heat transfer efficiency relative to the base fluid. The aforementioned improvement is more pronounced in the case of higher gap ratios and higher nanoparticle volume fractions.

Numerical Simulation of the Effect of a Single Gust on the Flow Past a Square Cylinder

The flow past a square cylinder under the influence of a one dimensional gust was investigated using computational fluid dynamics (CFD). The effect of upstream wind gusts of the same amplitude but different duration was investigated with respect to their effect on the flow, the vortex-shedding, and the pressure distribution around the square cylinder. For the computations, a very large eddy simulation (VLES) model was implemented in an in-house code and validated against numerical and experimental results from the literature. The gusts of different duration were found to have a distinctly different effect. The short-duration gust causes a lock-on behavior with cessation of the alternating vortex shedding, and a symmetric pair-vortex was created above and below the square cylinder. It was observed that the pressure distribution on the lateral sides of the cylinder has the same magnitude and phase, which resulted in a zero total lift coefficient. In terms of a free-standing structures, such as a building, this would lead to zero instantaneous forces and pressure difference in the lateral direction with obvious implications for dynamic response and cross ventilation.

Comparative study of hatchback vehicles through modelling and computational tools

The purpose of this research is to explore the world of Computer-Aided Modelling and then apply its tools to benefit the automotive sector. Three commercially available economical vehicles in Pakistan, namely (i) Daihatsu Mira X, (ii) Honda N-One and (iii) Suzuki Wagon R, have been virtually modelled in Computer-Aided Design (CAD) software by using CATIA-V5R19. This research focuses on providing all the steps that are needed to transform an existing real vehicle body to a virtual vehicle body. Detailed comparisons of all the three hatchback vehicles have performed which determined the most crucial factors of the body that affect the performance of the vehicle. Computational fluid dynamics (CFD) analysis is also performed using SolidWorks flow simulation tool. The base drag and lift coefficients of selected vehicles are computed and compared. Furthermore, the influence of different diffuser angles on the aerodynamics characteristics of vehicle is also investigated. The drag and lift coefficients are computed at different diffuser angles to find out the optimum angle of diffuser. With the increase in diffuser angle, it is found that the total lift coefficient decreases but there is not much effect on drag coefficient for all hatchback vehicles. In addition, this study revealed that Daihatsu Mira X is the most stable and fuel economic vehicle among all three considered vehicles because of its lower centre of gravity co-ordinates and smaller coefficient of drag values at all diffuser angles.

A numerical study of two-dimensional laminar flow of power-law fluids around three circular cylinders in side-by-side arrangement

PurposeThis study aims at investigating two-dimensional laminar flow of power-law fluids around three unconfined side-by-side cylinders.Design/methodology/approachThe numerical study is performed by solving the governing (continuity and momentum) equations using a finite volume-based code ANSYS Fluent. The numerical results have been presented for different combinations of the governing dimensionless parameters (dimensionless spacing, 1.2 = L = 4; Reynolds number, 0.1 = Re = 100; power-law index, 0.2 = n = 1.8). The dependence of the kinematic and macroscopic characteristics of the flow such as streamline patterns, distribution of the surface pressure coefficient, total drag coefficient with its components (pressure and friction) and total lift coefficient on these dimensionless parameters has been discussed in detail.FindingsIt is found that the separation of the flow and the apparition of the wake region accelerate as the dimensionless spacing decreases, the number of the cylinder increases and/or the fluid behavior moves from shear-thinning to Newtonian then to shear-thickening behavior. In addition, the distribution of the pressure coefficient on the surface of the cylinders presents a complex dependence on the fluid behavior index and Reynolds number when the dimensionless spacing between two adjacent cylinders is varied. At low Reynolds numbers, the drag coefficient of shear-thinning fluids is stronger than that of Newtonian fluids; this tendency decreases progressively with increasing of Re until a critical value; beyond the critical Re, the opposite trend is observed. The lift coefficient of the middle cylinder is null, whereas, the exterior cylinders experience opposite lift coefficients, which show a complex dependence on the dimensionless spacing, the Reynolds number and the power-law index.Originality/valueThe flow over bluff bodies is a practical engineering problem. In the literature, it can be seen that the previous studies on non-Newtonian fluids are limited to the flow over one or two cylinders (effect of an odd number of cylinders on each other). Besides that, the available results concerning the flow of Newtonian fluids over three cylinders are limited to the high Reynolds numbers region only. However, this work treats the flow of non-Newtonian power-law fluids past three circular cylinders in side-by-side arrangements under a wide range of Re. The outcome of the present study demonstrates that the augmentation of the geometry complexity to three cylinders (effect of pair surrounding cylinders on the surrounded ones in what concerns Von Karman Street phenomenon) causes a drastic change in the flow patterns and in the macroscopic characteristics. The present results may be used to predict the flow behavior around multiple side-by-side cylinders.

Pitch/Plunge Equivalence for Dynamic Stall of Swept Finite Wings

A high-fidelity numerical study is undertaken to expand the notion of pitch/plunge equivalence to finite, swept wings undergoing deep-dynamic stall and builds upon the analysis of straight wings in another paper by the authors [“Pitch/Plunge Equivalence for Dynamic Stall of Unswept Finite Wings,” AIAA Journal (submitted for publication)]. The wing has an aspect ratio of with a NACA 0012 section, a rounded tip, and a sweep angle of ; it operates at a Reynolds number of and a Mach number of . Equivalent pure-pitch and pure-plunge motions at two different reduced frequencies are considered to assess pitch-induced apparent camber on the wing and its effects on the three-dimensional flow structure, surface topology, and aerodynamic loading. Regardless of the motion type or rate, the wing undergoes dynamic tip stall that is initiated through the outboard separation of a dynamic stall vortex as it lifts off the surface and forms into an arch vortex before ejecting into the wake. The pitching cases exhibit an advanced development and evolution in time of these features that are observed as variable amplifications of the aerodynamic loading, which is due predominantly to an apparent camber effect. Corrections to the total and sectional lift and moment coefficients are explored by extending steady thin-airfoil theory to pitching swept wings. Remarkably, the corrected plunge-equivalent histories provide a full collapse of the force and moment responses between the pitching and plunging cases, despite the delayed behavior of the flow structure. This equivalence and the similar process of dynamic stall should facilitate the comparison of experiments and/or simulations employing different motion types, even for finite-aspect-ratio and swept wings.

Aerodynamic Characteristics of Coupled Twin Circular Bridge Hangers with Near Wake Interference

Much work has been devoted to the investigation and understanding of the flow-induced vibrations of twin cylinders vibrating individually (e.g., vortex-induced vibration and wake-induced galloping), but little has been devoted to coupled twin cylinders with synchronous galloping. The primary objective of this work is to investigate the aerodynamic forcing characteristics of coupled twin cylinders in cross flow and explore their effects on synchronous galloping. Pressure measurements were performed on a stationary section model of twin cylinders with various cylinder center-to-center distances from 2.5 to 11 diameters. Pressure distributions, reduced frequencies and total aerodynamic forces of the cylinders are analyzed. The results show that the flow around twin cylinders shows two typical patterns with different spacing, and the critical spacing for the two patterns at wind incidence angles of 0° and 9° is in the range of 3.8D~4.3D and 3.5D~3.8D, respectively. For cylinder spacings below the critical value, vortex shedding of the upstream cylinder is suppressed by the downstream cylinder. In particular, at wind incidence angles of 9°, the wake flow of the upstream cylinder flows rapidly near the top edge and impacts on the inlet edge of the downstream cylinder, which causes a negative and positive pressure region, respectively. As a result, the total lift force of twin cylinders comes to a peak while the total drag force jumps to a higher value. Moreover, there is a sharp drop of total lift coefficient for α = 9–12°, indicating the potential galloping instability. Finally, numerical simulations were performed for the visualization of the two flow patterns.

Numerical investigation on fluid forces of piggyback circular cylinders in tandem arrangement at low Reynolds numbers

Numerical simulations of flows past the piggyback circular cylinders in tandem arrangement are performed by solving the variational multiscale formulation of the incompressible Navier–Stokes equations using in-house finite element method (FEM) codes. The effects of the gap-spacing-to-diameter (G/D) and the two diameter ratio (d/D) on the flow characteristics and the reductions of the root-mean-square (RMS) drag and lift coefficients are considered for Reynolds numbers (Res) are 100 and 200. The validation shows the fluid force coefficients obtained by the in-house FEM codes are in good agreement with the results in the existing literatures. The obtained results show that, with a proper placement of the smaller cylinder ( $$d/D=0.2$$ ) behind the larger cylinder, the RMS drag and lift coefficients largely decrease compared to those of the single circular cylinder. When $$d/D=0.2$$ , the largest reductions of the RMS lift coefficient of the larger cylinder and the RMS total lift coefficient appear at $$G/D=1.2$$ as Re $$=100$$ and at $$G/D=1.0$$ as Re $$=200$$ . It is observed that the proper placement of the smaller cylinder causes the surrounding vorticity to take opposite sign with the vorticity in the outer region so as to suppress and postpone the vortex shedding in the wake, and that the different positions of the vortex shedding at two Res cause that the largest reductions of the RMS lift coefficient of the larger cylinder and the RMS total lift coefficient appear at different G/D as Re is different. When d/D varies, the variation of the RMS total lift coefficient behaves differently at two Res. It decreases with d/D increasing at Re $$=100$$ , while it no longer monotonously varies with d/D, but reaches a minimum in the considered range of d/D at Re $$=200$$ . Moreover, the larger d/D results in stronger suppression and postponement of the vortex shedding in the wake. The effects of the gap-spacing-to-diameter and the two-diameter ratio on the flow characteristics and the reductions of the root-mean-square (RMS) drag and lift coefficients are investigated by stabilized finite element method. With a proper placement of the smaller cylinder behind the larger cylinder, the RMS drag and lift coefficients are smaller than those of the single circular cylinder. The proper placement of the smaller cylinder causes the surrounding vorticity to take opposite sign with the vorticity in the outer region so as to suppress and postpone the vortex shedding in the wake.

Flow around a surface-mounted finite circular cylinder completely submerged within the bottom boundary layer

This paper presents a detailed investigation on the flow characteristics and the bed-shear-stress distribution around a finite circular cylinder at a fixed Reynolds number (Re= 2 ×104) and seven aspect ratios (AR= 0.5∼6) by solving the Reynolds Averaged Navier–Stokes (RANS) equations. It is found that, for a moderate Reynolds number and a relatively large boundary-layer thickness, the time-averaged streamwise vortex structure will be transformed from the ‘Dipole Type’ at AR≤3 to the ‘Three-Pairs Type’ at AR≥4. It is the first time that the ‘Three-Pairs Type’ vortex structure has been reported, which consists of Time-Mean Streamwise Tip Vortices, Time-Mean Streamwise Base Vortices and Time-Mean Streamwise Bottom Vortices. Besides, this study indicates that, with increasing AR, the maximum time-averaged bed-shear-stress amplification magnitude upstream of the cylinder will first decrease and then increase, with the minimum occurring at approximately AR= 3.0, due to the influence of AR on the horseshoe vortices. Additionally, this study manifests that different critical AR values can be obtained for various flow variables. For instance, in terms of the total lift coefficient of the cylinder and the transverse fluctuating velocity in the symmetry plane at the mid-height of the cylinder, the critical AR is equal to ARc=3.0 and ARc=2.0, respectively.

The double‐tree method: An O(n) unsteady aerodynamic lifting surface method

SummaryTwo new methods for reducing the computational cost of the unsteady vortex lattice method are developed. These methods use agglomeration to construct time‐saving tree structures by approximating the effect of either a group of vortex rings or query points. A case study shows that combining the two new O(n·log n) tree methods together results in an O(n) method, called the double‐tree method. Other case studies show that the trade‐off between accuracy and speed can be easily and reliably controlled by the agglomeration cutoff distance. For a flat plate with 5 × 200 panels analyzed over 20 time steps, the double‐tree method is 7 times faster than the unsteady vortex lattice method with a <5% difference in the force distribution and total lift coefficient. The case studies suggest that the computational benefit will increase for the same level of accuracy if the size of the problem is increased, making the method beneficial for full‐aircraft analysis within optimization or dynamic load analysis, where the computational cost of the unsteady vortex lattice method can be large.

On the transition behavior of laminar flow through and around a multi-cylinder array

We numerically investigated the transitional behavior of two-dimensional laminar flows through and around a square array of 100 circular cylinders. The solid fraction of the array ϕ ranged from 0.007 85 to 0.661 and the Reynolds number Re (based on the free-stream velocity and the side length of the array) varied from 40 to 200. Globally, the first transition appears at the onset of vortex shedding, where the critical Reynolds number Recr is estimated from the Stuart-Landau equation. The results show that Recr ranges from 40 to ∼45 for the investigated range of ϕ. It is found that Recr increases quadratically with ϕ and the critical Reynolds number for an individual cylinder (Rdcr) increases linearly with ϕ. The subsequent transitions largely depend on ϕ, as revealed from the total drag and lift coefficients, Strouhal number, and the instantaneous vorticity field. For sufficiently small ϕ at high Re, the global vortex shedding is suppressed due to the weakened interaction between cylinders in the array. Several more cases with ϕ of 0.007 85 for Re between 400 and 4000 are also calculated to visualize the suppression behavior. The global transition behaviors are closely related to the secondary frequency (SF) observed from the power spectra of the local velocity. It is highly possible that the SF results from the cylinder interaction in the array. The local instabilities induced by cylinder interactions would promote the onset of global vortex shedding at small Re. Also, the local instabilities still exist even though the global vortex shedding is suppressed at large Re.

Analysis of Influencing Factors on Lift Coefficients of Autonomous Sailboat Double Sail Propulsion System Based on Vortex Panel Method

Sail is the core part of autonomous sailboat and wing sail is a new type of sail. Wing sail generates not only propulsion but also lateral force and heeling moment. The latter two will affect the navigation status and bring resistance. Double sail can effectively reduce the center of wind pressure and heeling moment. In order to study the effect of distance between two sails, airfoil and attack angle on the total lift coefficient of double sail propulsion system, pressure coefficient distribution and lift coefficient calculation model have been established based on vortex panel method. By using the basic finite solution, the fluid dynamic forces on the two-dimensional sails are computed. The results show that, the distance in the range of 0 to 1 time chord length, when using the same airfoil in the fore and aft sail, the total lift coefficient of the double sail increases with the increase of distance, finally reaches a stable value in the range of one to three times chord length. Lift coefficients of thicker airfoils are more sensitive to the change of distance. The thicker the airfoil, the longer distance is required of the total lift coefficient toward stable. When different airfoils are adopted in fore and aft sail, the total lift coefficient increases with the increase of the thickness of aft sail. The smaller the thickness difference is, the more sensitive to the distance change the lift coefficient is. The thinner the fore sail is, the lower the influence will be on the lift coefficient of aft sail.

Aerodynamic interaction of collective plates in side-by-side arrangement

In the tip-reversal upstroke of avian flight, individual feathers twist so as to create gaps between them. Although this behavior allows the feathers to function as individual lift-generating bodies, the lift generation mechanism of these multiple bodies remains unclear. This paper reports a numerical investigation of multiple stationary plates arranged side by side in a uniform flow. The aim is to elucidate the collective mechanism of the flow generated by the plates and the lift contribution of each plate. The angle of attack of each plate and the gap between the plates are varied to determine their influence on the flow and lift of the collection of plates. The time-averaged lift increases from the lowermost to the uppermost plate, and, at a high angle of attack, the total lift coefficient of the plates becomes greater than that of a single plate solely placed in a uniform flow. At a high angle of attack, vortex shedding from the upper plates is synchronized with some phase difference, resulting in synchronized lift fluctuations for individual plates and a reduction in the overall fluctuation amplitude. With an optimal gap ratio and angle of attack, the collective behavior of plates in side-by-side arrangement can be advantageous to enhance lift-generation performance.

Optimal performance of adaptive flap on flow separation control

The stall caused by flow separation of airfoil seriously compromises the efficiency and safety of wind turbines. Inspired by bird feathers, a passive flow control strategy was investigated by configuring adaptive flaps on the suction surface of the airfoil to delay flow separation. The Computational Fluid Dynamics (CFD) software ANSYS Fluent 17.0 using SST k–ω turbulence model was performed to study the performance of the adaptive flap with different length and location. The performance was evaluated by the comparison of total lift coefficient between the flap airfoil and clean airfoil. In addition, the performance of the double flaps configuration was investigated by Fluid-Solid Interaction (FSI) method. The results show that when the separation point is at the upstream of flap hinge point, the total lift coefficient increases with the flap rising, and when the flap reaches the optimal flap angle, the lift coefficient begins to decrease. When the flap operates in optimal angle, the closer the flap is to the trailing edge of the airfoil, the more the lift enhancement for moderate flow separation, and the closer the flap is to the leading edge of the airfoil, the more the lift enhancement for serious flow separation. For the flaps with the same location, the longer flap can block more backflow resulting in a better performance, but when the flap is long enough to block the fluid, the shorter flap has better performance. Considering the variations of the flap aerodynamic moment with the flap angle, an external hinge moment was recommended to improve the swinging flap performance.

On the Wake Properties of Segmented Trailing Edge Extensions

Changes in the amount and the distribution of mean and turbulent quantities in the free shear layer wake of a 2D National Advisory Committee for Aeronautics (NACA) 0012 airfoil and an AR 4 NACA 0012 wing with passive segmented rigid trailing edge (TE) extensions were investigated at the University of Dayton Low Speed Wind Tunnel (UD-LSWT). The TE extensions were intentionally placed at zero degrees with respect to the chord line to study the effects of segmented extensions without changing the effective angle of attack. Force based experiments were used to determine the total lift coefficient variation of the wing with seven segmented trailing edge extensions distributed across the span. The segmented trailing edge extensions had a negligible effect on the lift coefficient, but showed a measurable decrement in the sectional and total drag coefficient. Investigation of turbulent quantities (obtained through Particle Image Velocimetry (PIV)) such as Reynolds stress, streamwise and transverse root-mean square (RMS) in the wake, reveal a significant decrease in magnitude when compared to the baseline. The decrease in the magnitude of turbulent parameters was supported by the changes in coherent structures obtained through two-point correlations. Apart from the reduction in drag, the lower turbulent wake generated by the extensions has implications in reducing structural vibrations and acoustic tones.

Study on the Aerodynamic Performance of the High-Speed Train Head with Symmetrical and Asymmetric Nose Shape

This study focused on the use of mesh morphing on optimizing high-speed train shape. Three shape variables were studied in this paper: the angle of cab-window, length of train-nose and width of train-nose. The original high-speed train head was optimized in symmetrical and asymmetric deformation. Total drag coefficient and lift coefficient of head car and tail car were optimized using Kriging model and NSGA- Ⅱ. As a result, three objective aerodynamic performance of the optimal train in symmetrical deformation is slightly improved comparing with the original ones and that in asymmetric deformation is improved significantly. Also, results of the symmetrical and asymmetric optimized high-speed train running in different speed were compared with that of the original high-speed train. Proposed method in this paper has been proved to be an efficient and feasible approach to study and optimize the aerodynamic performance of different high-speed trains as well as other structures.

Numerical study of flow-induced oscillations of two rigid plates elastically hinged at the two ends of a stationary plate in a cross-flow

The flow-induced oscillation (FIO) of bluff bodies is commonly encountered in the fluid structure interaction (FSI) problems. In this study, we use an unstructured moving grid strategy and simulate the FIO of two rigid plates, which are elastically hinged at the two ends of a fixed flat plate in a cross-flow. We use a hybrid finite-element-volume (FEV) method in an arbitrary Lagrangian–Eulerian (ALE) framework to study FIO of the two hinged plates. The current simulations are carried out for wide ranges of flow Reynolds number (50–175), spring stiffness coefficient, and the two hinged plates' moment of inertia magnitudes. The influences of these parameters are investigated on the magnitudes of maximum deflection angle, the amplitude of oscillation, the total lift and drag coefficients, and so on. The study is also carried out in the transition period to describe the in-phase and out-of-phase angular oscillations occurring for the two elastically hinged plates with respect to each other. After the transition period, the two hinged plates eventually arrive to a similar periodic oscillation; however, with some phase lags. We find that the achieved phase lag is equal to the phase lag between the two pairs of flow vortices, which are alternatively shed into the flow from the upper and lower hinged plates. Similar to past FIO problems, the current model also exhibits two important lock-in and phase-switch FSI phenomena; however, in angular directions. There is a phase jump of approximately 170° between the aerodynamic lift coefficient and angular oscillations of hinged plates, which nearly occurs in the middle of lock-in region. Indeed, our literature review shows that this is the first time to report the phase-switch phenomenon in angular oscillations of three-element bluff bodies in a FSI problem.

Characteristics of aerodynamic forces exerted on a twisted cylinder at a low Reynolds number of 100

Laminar flow over a twisted cylinder is numerically simulated at a Reynolds number of 100. The flow past a smooth cylinder is calculated for comparison. Jung and Yoon (J. Fluid Mech., 759, 2014) showed the considerable suppression of force coefficients at the subcritical Reynolds number of 3000. The present results verify that the twisted shape of the cylinder can be used to reduce the force coefficients at a low Reynolds number containing the laminar flow. This suppression of the force coefficients is supported by a longer vortex formation length produced by the twisted cylinder. We investigated the characteristics of the local force coefficients for a twisted cylinder. The simple periodic oscillation of the time histories of total and local lift coefficients for the twisted cylinder exhibits the same pattern as that of a smooth cylinder. However, the time history of drag for the twisted cylinder reveals the presence of multi-frequency oscillations, resulting in harmonic behavior of the power spectra. This is confirmed by a time sequence of the instantaneous flow fields during the half-period of the time histories of force coefficients. The nature of the three-dimensional (3-D) twisted shape forms the 3-D vortical structures along the spanwise direction, which leads to the harmonic behavior of the drag time trace power spectra.

Computational aerodynamic modeling for flight dynamics simulation of ram-air parachutes

This work presents a step toward bridging the gap between flight dynamics simulation of ram-air parachutes and high-fidelity computational fluid dynamics. Today's parachute design codes mainly rely on the empirical or semi-empirical methods generated from wind tunnel experiments and drop tests. The outcome of this study will hopefully help to reduce the cost of experiments and drop testing in the design of future canopies and to better understand the aerodynamic characteristics of these geometries. In this work, the parachute geometries were modeled as rigid rectangular wings with an aspect ratio of two and zero anhedral angle. The wings have seven opening cells and the trailing edge is deflected or not deflected. To validate computational methods, the aerodynamic predictions of similar wings, but with closed and round inlets, are compared with experimental data available from the Subsonic Wind Tunnel at United States Air Force Academy. Total lift and drag force coefficients were measured at a Reynolds number of 1.4 million. The results show that computational predictions of fine (closed-inlet) grids match the experimental data very well up to the stall angle. Both experiments and simulations show that closed wings have sharp stalling characteristics. The aerodynamics of closed wings up to stall can be approximated by linear functions and their derivatives. The closed wings show a negative static stability with respect to changes in the angle of attack. The open wings, on other hand, have positive static stability in the longitudinal and lateral directions. The open wings exhibit highly nonlinear unsteady aerodynamic characteristics; they also stall earlier and have higher drag values than the closed wings. The aerodynamic derivatives of open and closed wings were estimated using a linear regression method and training data simulated in small-amplitude oscillations in pitch, yaw, and roll directions. While the open wings have large oscillations in aerodynamic coefficients over the yawing and rolling hysteresis loops, lateral aerodynamic derivatives of the open and closed wings are similar. Finally, the results show that model predictions are reasonably accurate for use in flight-dynamics simulations.

Numerical study on the 3-D complex characteristics of flow around the hull structure of TLP

Vortex-induced motion is based on the complex characteristics of the flow around the tension leg platform (TLP) hull. By considering the flow field of the South China Sea and the configuration of the platform, three typical flow velocities and three flow directions are chosen to study the numerical simulation of the flow field characteristics around the TLP hull. Reynolds-averaged Navier–Stokes equations combined with the detached eddy simulation turbulence model are employed in the numerical study. The hydrodynamic coefficients of columns and pontoons, the total drag and lift coefficients of the TLP, the formation and development of the wake, and the vorticity iso-surfaces for different inlet velocities and current directions are discussed in this paper. The average value of the drag coefficient of the upstream columns is considerably larger than that of the downstream columns in the inlet direction of 0°. Although the time history of the lift coefficient demonstrates a “beating” behavior, the plot shows regularity in general. The Strouhal number decreases as the inlet velocity increases from the power spectral density plot at different flow velocities. The mean root values of the lift and drag coefficients of the front column decrease as the current direction increases. Under the symmetrical configuration of 45°, the streamwise force on C4 is the smallest, whereas the transverse force is the largest. The broken vortex conditions in current directions of 22.5° and 45° are more serious than that in the current direction of 0°. In addition, turbulence at the bottom of the TLP becomes stronger when the current direction changes from 0° to 45°. However, a high inlet velocity indicates a large region influenced by the broken vortex and shows the emergence of the wake behind the TLP under the same current angle.

Wall effects on the cross-buoyancy around a square cylinder in the steady regime

The effects of blockage ratio on the combined free and forced convection from a long heated square obstacle confined in a horizontal channel are investigated in this work. The numerical computations are performed in the steady regime for Reynolds number = 1 - 30, Richardson number = 0 - 1 for blockage ratios of 0.125 and 0.25 for the fixed Prandtl number of 0.7 (air). The governing equations, along with appropriate boundary conditions, are solved by using a semi-explicit finite volume method implemented on the collocated grid arrangement. The total drag and lift coefficients, local and average Nusselt numbers and the representative streamline, vorticity and isotherm patterns are presented to elucidate the role of blockage ratio on the cross-buoyancy across a confined square cylinder. The asymmetry in the flow and temperature fields decreases with increasing value of the blockage ratio. Similar to forced convection, the total drag coefficient increases with increasing value of the blockage ratio for the fixed values of the Reynolds and Richardson numbers.